SNN-Genesis v14: Stochastic Resonance in LLM Reasoning — Reasoning Manifold Geometry, Orthogonal Complement Noise, and Dimensional Annealing

SNN-Genesis v14 discovers the geometry of the reasoning manifold and explains why random noise works for stochastic resonance in LLM reasoning. NEW in v14 (Season 15, Phases 77, 71, 78, 79): Honest Correction (Phase 77): v13's recovery-only +10pp effect does not replicate at N=100 (Fisher p=0.24). Flash Annealing (34%, p<10⁻⁵) and all-on (26%, p<0.001) remain highly significant. Reasoning Manifold Geometry (Phase 71): PCA-top-4 noise (aligned with the principal components of reasoning) achieves only 6.7% = baseline. The reasoning axis is encoded in the top PCs; perturbing them destroys reasoning. Random noise naturally avoids this axis in 4096-D. 50% All-Time Record (Phase 78): Full-rank (k=4096) noise with Flash Annealing achieves 50%, surpassing the previous record of 46%. Dual annealing (σ + k decay) matches at 50%. Orthogonal Complement = Random (Phase 79): Projecting out top-4 PCs has zero effect (46.7% = random). In 4096-D, random noise has only 0.098% overlap with the 4-D reasoning axis. PCA-top-4-only collapses to 3.3%. Random noise is "naturally safe." From v13 (retained): Low-Rank Noise Efficiency (Phase 70b): k=256 matches full-rank; k=4 achieves 5× baseline Semantic Phase Decomposition (Phase 76): Flash Annealing 30.0% > all-on semantic 23.3% Noise Source Invariance (Phase 70c, honest null result) 1/√N dose law, 40% at N=100, Flash Annealing 82 page paper. Full experimental code and data included. Code: https://github.com/hafufu-stack/snn-genesis